A circle has a circumference of $20\pi$. It has an arc of length $\dfrac{32}{3}\pi$. What is the central angle of the arc, in radians? ${20\pi}$ ${\dfrac{16}{15}\pi}$ $\color{#DF0030}{\dfrac{32}{3}\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{\theta}{2 \pi} = \dfrac{32}{3}\pi \div 20\pi$ $\dfrac{\theta}{2 \pi} = \dfrac{8}{15}$ $\theta = \dfrac{8}{15} \times 2 \pi$ $\theta = \dfrac{16}{15}\pi$ radians